STOCHASTIC

26 THE REVIEW OF ECONOMICS AND STATISTICS
Vm — the aggregate market value of the
j th stock at time zero,
&i — the aggregate return on the i' h stock
(the sum of aggregate cash dividends paid
and appreciation in aggregate market
value over the transaction period); and
T = 2, Vat, the aggregate market value
of all stock in the market at time zero.
The original economic definitions of the variables
in the portfolio optimization problem give
(26a) hi = VK/T,
(266) ti = Ri/VK,
(26c) Xi = fi - r* = (Ri - r* Ko()/Voi,
(26d) ±i, = fa = R,j/V,i VOJ,
where Rti is the covariance of the aggregate dollar
returns of the i th and j tk stocks (and Ra is the
i th stock's aggregate return variance). The equilibrium
conditions (12) may now be written
, . Ri - r* V* , V," R«
(12a) = X — .
Voi T (v„,y
which reduces to
(27) Ri - r* V,t = (X/T) [Ra + 2*f Ri,]
= (X/r)M